By John D. Wagner
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17b) where u and v are the displacement components in the x- and y-directions, respectively. 18b) ε y = −ν where ν is Poisson’s ratio. 21b) −h / 2 h/2 My = y −h / 2 25 The Era of Elasticity In this regard, the twisting moments, Mxy and Myx, and shearing forces, Qx and Qy, cannot be considered as generalized stresses since the deformations associated with their correspondent stresses are negligible. 4 Shell Element as a Further Extension The most common shell structures are thin cylindrical shells under axisymmetric loading, as in water tanks, towers, etc.
95b) ∑ of beam stiffnesses meeting at joint B The indices b and c stand for beam and column, respectively, and the indices A and B stand for joints A and B, respectively. 21). 22). The first example is a frame where sway is not allowed and the second example is a frame where sway is allowed. 22a, where sway is assumed to be prevented. The deflected shape of the frame is assumed as illustrated by the dashed lines. 96) The index c stands for column. 97) The index b stands for beam. 21 Alignment charts: (a) braced system and (b) unbraced system.
For instance, the critical load of a system can be determined by the slope-deflection equations or a second-order analysis. On the other hand, the value of the K factor can be assessed with the aid of the alignment charts that are derived from the slope-deflection method. 2 Alignment Charts The alignment charts have been developed by Julian and Lawrence (1959) for a simplified assessment of the K factor. 20 are used for a system that is braced against side sway and an unbraced system. In both models, the following assumptions are adopted: 1.